Problem: Divide the polynomials.
Solution: Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. $\begin{array}{r} x+7 \\ x-1|\overline{x^2+6x-4} \\ \mathllap{-(}\underline{x^2-\phantom{6}x\phantom{-4}\rlap )} \\ 7x-4 \\ \mathllap{-(}\underline{7x-7\rlap )} \\ 3 \end{array}$ We get that the quotient is $x+7$ and the remainder is $3$, and therefore: $\dfrac{x^2+6x-4}{x-1}=x+7+\dfrac{3}{x-1}$ [I want to see a different way of performing the division.]